Stability of the viscous fluid film flow on a uniformly heated substrate

The linear stability is investigated of a viscous fluid film on a uniformly heated substrate under an arbitrary angle of inclination against the horizon. At the substrate, the heat flux is set; at the film surface, the fluid-gas heat transfer coefficient is specified. The waves are considered in the film propagating in an arbitrary direction. Within the frame of the integral model, the dispersion ratios are obtained for the wave increment and phase velocity. The analysis is performed of the dispersion ratios, and the flow instability range is determined. At the Marangoni numbers above a certain threshold, standing wave or traveling wave type disturbances take place; the waves increase in the horizontal direction. For the traveling waves, the Marangoni number threshold value is significantly lower than the same for the standing waves.